We will discuss the Area and perimeter of a sector of a circle
We know that
Therefore,
Area of a sector of a circle = θ∘360∘ × Area of the circle = θ360 ∙ πr2
where r is the radius of the circle and θ∘ is the sectorial angle.
Also, we know that
Therefore,
Arc MN = θ∘360∘ × Circumference of the circle = θ360 ∙ 2πr = πθr180
where r is the radius of the circle and θ∘ is the sectorial angle.
Thus,
perimeter of a sector of a circle = (πθ180 ∙ r + 2r) = (πθ180 + 2)r
where r is the radius of the circle and θ° is the sectorial angle.
Problems on Area and Perimeter of a Sector of a Circle:
1. A plot of land is in the shape of a sector of a circle of radius 28 m. If the sectorial angle (central angle) is 60°, find the area and the perimeter of the plot. (Use π = 227.)
Solution:
Area of the plot = 60∘360∘ × πr2 [Since θ = 60]
= 16 × πr2
= 16 × 227 × 282 m2.
= 16 × 227 × 784 m2.
= 1724842 m2.
= 12323 m2.
= 41023 m2.
Perimeter of the plot = (πθ180 + 2)r
= (227 ∙ 60180 + 2) 28 m
= (2221 + 2) 28 m
= 6421 ∙ 28 m
= 179221 m
= 2563 m
= 8513 m.
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